IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v89y2019i2d10.1007_s00186-018-0648-y.html
   My bibliography  Save this article

Optimal exchange rates management using stochastic impulse control for geometric Lévy processes

Author

Listed:
  • Jinbiao Wu

    (Central South University)

Abstract

In this paper, we consider the optimal impulse control problem of a currency with exchange rate dynamics whose state follows a geometric Lévy process. The objective of the Central Bank is to keep the exchange rate as close as possible to a given target. Running costs associating with the difference between the actual exchange rate and the target are continuously incurred to the system. We suppose that, when the Central Bank intervenes in the system, it requires the fixed and proportional costs. Applying the theory of stochastic impulse controls, we find the optimal exchange rate at which interventions should be performed and the optimal sizes of the interventions, so as to minimize the expected total discounted sum of the intervention costs and running costs incurred over the infinite time horizon. Furthermore, numerical comparisons for the optimal intervention strategy between the geometric Lévy process model and the geometric Brownian motion model are investigated in details.

Suggested Citation

  • Jinbiao Wu, 2019. "Optimal exchange rates management using stochastic impulse control for geometric Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 257-280, April.
    • Handle: RePEc:spr:mathme:v:89:y:2019:i:2:d:10.1007_s00186-018-0648-y
    DOI: 10.1007/s00186-018-0648-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-018-0648-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-018-0648-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Abel Cadenillas & Sudipto Sarkar & Fernando Zapatero, 2007. "Optimal Dividend Policy With Mean‐Reverting Cash Reservoir," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 81-109, January.
    2. George M. Constantinides, 1976. "Stochastic Cash Management with Fixed and Proportional Transaction Costs," Management Science, INFORMS, vol. 22(12), pages 1320-1331, August.
    3. J. Michael Harrison & Thomas M. Sellke & Allison J. Taylor, 1983. "Impulse Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 454-466, August.
    4. Haolin Feng & Kumar Muthuraman, 2010. "A Computational Method for Stochastic Impulse Control Problems," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 830-850, November.
    5. Agnès Sulem, 1986. "A Solvable One-Dimensional Model of a Diffusion Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 125-133, February.
    6. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
    7. Melda Ormeci & J. G. Dai & John Vande Vate, 2008. "Impulse Control of Brownian Motion: The Constrained Average Cost Case," Operations Research, INFORMS, vol. 56(3), pages 618-629, June.
    8. Ricardo Huamán-Aguilar & Abel Cadenillas, 2015. "Government Debt Control: Optimal Currency Portfolio and Payments," Operations Research, INFORMS, vol. 63(5), pages 1044-1057, October.
    9. Ralf Korn, 1997. "Optimal Impulse Control When Control Actions Have Random Consequences," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 639-667, August.
    10. Ohnishi, Masamitsu & Tsujimura, Motoh, 2006. "An impulse control of a geometric Brownian motion with quadratic costs," European Journal of Operational Research, Elsevier, vol. 168(2), pages 311-321, January.
    11. Daniel Mitchell & Haolin Feng & Kumar Muthuraman, 2014. "Impulse Control of Interest Rates," Operations Research, INFORMS, vol. 62(3), pages 602-615, June.
    12. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
    13. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
    14. George M. Constantinides & Scott F. Richard, 1978. "Existence of Optimal Simple Policies for Discounted-Cost Inventory and Cash Management in Continuous Time," Operations Research, INFORMS, vol. 26(4), pages 620-636, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Perera, Sandun & Gupta, Varun & Buckley, Winston, 2020. "Management of online server congestion using optimal demand throttling," European Journal of Operational Research, Elsevier, vol. 285(1), pages 324-342.
    2. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
    3. Daniel Mitchell & Haolin Feng & Kumar Muthuraman, 2014. "Impulse Control of Interest Rates," Operations Research, INFORMS, vol. 62(3), pages 602-615, June.
    4. Matteo Basei, 2018. "Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates," Papers 1803.08166, arXiv.org, revised Mar 2019.
    5. Haolin Feng & Kumar Muthuraman, 2010. "A Computational Method for Stochastic Impulse Control Problems," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 830-850, November.
    6. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
    7. Matteo Basei, 2019. "Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 355-383, June.
    8. Sandun Perera & Winston Buckley & Hongwei Long, 2018. "Market-reaction-adjusted optimal central bank intervention policy in a forex market with jumps," Annals of Operations Research, Springer, vol. 262(1), pages 213-238, March.
    9. Sandun Perera & Winston Buckley, 2017. "On the existence and uniqueness of the optimal central bank intervention policy in a forex market with jumps," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(8), pages 877-885, August.
    10. Shuangchi He & Dacheng Yao & Hanqin Zhang, 2017. "Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 979-1006, November.
    11. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    12. Jingchen Wu & Xiuli Chao, 2014. "Optimal Control of a Brownian Production/Inventory System with Average Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 163-189, February.
    13. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    14. Fernando Alvarez & Francesco Lippi & Roberto Robatto, 2019. "Cost of Inflation in Inventory Theoretical Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 32, pages 206-226, April.
    15. Lu Xiao & Huacong Ding & Yu Zhong & Chaojie Wang, 2023. "Optimal Control of Industrial Pollution under Stochastic Differential Models," Sustainability, MDPI, vol. 15(6), pages 1-16, March.
    16. Ohnishi, Masamitsu & Tsujimura, Motoh, 2006. "An impulse control of a geometric Brownian motion with quadratic costs," European Journal of Operational Research, Elsevier, vol. 168(2), pages 311-321, January.
    17. Alain Bensoussan & Benoît Chevalier-Roignant, 2019. "Sequential Capacity Expansion Options," Operations Research, INFORMS, vol. 67(1), pages 33-57, January.
    18. Zhen Xu & Jiheng Zhang & Rachel Q. Zhang, 2019. "Instantaneous Control of Brownian Motion with a Positive Lead Time," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 943-965, August.
    19. Melda Ormeci & J. G. Dai & John Vande Vate, 2008. "Impulse Control of Brownian Motion: The Constrained Average Cost Case," Operations Research, INFORMS, vol. 56(3), pages 618-629, June.
    20. Gregory Gagnon, 2019. "Vanishing central bank intervention in stochastic impulse control," Annals of Finance, Springer, vol. 15(1), pages 125-153, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:89:y:2019:i:2:d:10.1007_s00186-018-0648-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.